Bulk Singularities and the Effective Cosmological Constant for Higher Co-dimension Branes

TL;DR

This paper investigates how bulk singularities influence the effective cosmological constant in higher co-dimension brane models, deriving relations between brane properties and observable curvature, and finding solutions with de Sitter or anti-de Sitter geometries.

Contribution

It provides a general relation connecting brane-induced curvature to bulk field asymptotics and explicitly solves the field equations for specific compactifications, revealing conditions for flat or curved observable dimensions.

Findings

Bulk singularities affect the effective cosmological constant.

Nonsingular or conically singular geometries lead to flat observable dimensions.

New solutions with de Sitter or anti-de Sitter 4D geometries in 6D supergravity.

Abstract

We study a general configuration of parallel branes having co-dimension >2 situated inside a compact d-dimensional bulk space within the framework of a scalar and flux field coupled to gravity in D dimensions, such as arises in the bosonic part of some D-dimensional supergravities. A general relation is derived which relates the induced curvature of the observable noncompact n dimensions to the asymptotic behaviour of the bulk fields near the brane positions. For compactifications down to n = D-d dimensions we explicitly solve the bulk field equations to obtain the near-brane asymptotics, and by so doing relate the n-dimensional induced curvature to physical near-brane properties. In the special case where the bulk geometry remains nonsingular (or only conically singular) at the brane positions our analysis shows that the resulting n dimensions must be flat. As an application of these results we specialize to n=4 and D=6 and derive a new class of solutions to chiral 6D supergravity for which the noncompact 4 dimensions have de Sitter or anti-de Sitter geometry.